An alternative method to construct the ML problem solution is generalized integral transform (GIT). The GIT method is used in physics, [1]}, [2]}, but was unknown in finance until its first use in [3]}. The previously known solution to the heat equation, using the GIT method, was obtained only for the domain \(S \in [0,y(t)]\) . For other domains, the solution was unknown even in physics. [4]} were the first to construct the GIT solution for the domain \(S \in [y(t), \infty )\) . The latter technique was extended further for the CIR and CEV models, [5]}, the Black-Karasinski model, [6]}, and finally for double barrier options in [7]}. The latter problem deals with the spatial domain determined by two moving in time boundaries, and boundary conditions, which are arbitrary functions of time.
